Platonic Solids and Their Programming: A Geometrical Approach

This work covers a three-week program designed to provide undergraduate students with a background in structural chemistry and materials science. Sessions are based on the programming of regular polyhedra and their geometrical relationships by using an object-oriented language (i.e., POV-Ray). Three lectures introduce the basics of programming (syntax), Platonic solids, and the geometrical study of metal clusters and carbon structures. Students work with geometrical aspects of two-dimensional (2D) polygons and generate computer-based algorithms. Next, students study dual three-dimensional (3D) polyhedral shapes, where they adapt the written code to generate Cartesian coordinates of the Platonic solids. Materials to guide the students include an explanation of pseudocodes, tutoring to accompany the programming sessions, reviews of generated codes, and session exercises and challenges. All activities during each hands-on session aim to engage and maintain the initial expectations of the students. Students gain capabilities and knowledge allowing them to code final tests: the C[subscript 60] molecule; an icosahedral metal cluster; and a cuboctahedron.